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dezoksy [38]
3 years ago
10

Simplify the expression (4y+1) (2) (FAST PEOPLE)​

Mathematics
1 answer:
AnnZ [28]3 years ago
8 0

Answer:

8y+2

Step-by-step explanation:

(4y+1)(2)

=(4y+1)(2)

=(4y)(2)+(1)(2)

=8y+2

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Firdavs [7]

Answer:

letter d

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5 0
3 years ago
Read 2 more answers
For each vector field f⃗ (x,y,z), compute the curl of f⃗ and, if possible, find a function f(x,y,z) so that f⃗ =∇f. if no such f
butalik [34]

\vec f(x,y,z)=(2yze^{2xyz}+4z^2\cos(xz^2))\,\vec\imath+2xze^{2xyz}\,\vec\jmath+(2xye^{2xyz}+8xz\cos(xz^2))\,\vec k

Let

\vec f=f_1\,\vec\imath+f_2\,\vec\jmath+f_3\,\vec k

The curl is

\nabla\cdot\vec f=(\partial_x\,\vec\imath+\partial_y\,\vec\jmath+\partial_z\,\vec k)\times(f_1\,\vec\imath+f_2\,\vec\jmath+f_3\,\vec k)

where \partial_\xi denotes the partial derivative operator with respect to \xi. Recall that

\vec\imath\times\vec\jmath=\vec k

\vec\jmath\times\vec k=\vec i

\vec k\times\vec\imath=\vec\jmath

and that for any two vectors \vec a and \vec b, \vec a\times\vec b=-\vec b\times\vec a, and \vec a\times\vec a=\vec0.

The cross product reduces to

\nabla\times\vec f=(\partial_yf_3-\partial_zf_2)\,\vec\imath+(\partial_xf_3-\partial_zf_1)\,\vec\jmath+(\partial_xf_2-\partial_yf_1)\,\vec k

When you compute the partial derivatives, you'll find that all the components reduce to 0 and

\nabla\times\vec f=\vec0

which means \vec f is indeed conservative and we can find f.

Integrate both sides of

\dfrac{\partial f}{\partial y}=2xze^{2xyz}

with respect to y and

\implies f(x,y,z)=e^{2xyz}+g(x,z)

Differentiate both sides with respect to x and

\dfrac{\partial f}{\partial x}=\dfrac{\partial(e^{2xyz})}{\partial x}+\dfrac{\partial g}{\partial x}

2yze^{2xyz}+4z^2\cos(xz^2)=2yze^{2xyz}+\dfrac{\partial g}{\partial x}

4z^2\cos(xz^2)=\dfrac{\partial g}{\partial x}

\implies g(x,z)=4\sin(xz^2)+h(z)

Now

f(x,y,z)=e^{2xyz}+4\sin(xz^2)+h(z)

and differentiating with respect to z gives

\dfrac{\partial f}{\partial z}=\dfrac{\partial(e^{2xyz}+4\sin(xz^2))}{\partial z}+\dfrac{\mathrm dh}{\mathrm dz}

2xye^{2xyz}+8xz\cos(xz^2)=2xye^{2xyz}+8xz\cos(xz^2)+\dfrac{\mathrm dh}{\mathrm dz}

\dfrac{\mathrm dh}{\mathrm dz}=0

\implies h(z)=C

for some constant C. So

f(x,y,z)=e^{2xyz}+4\sin(xz^2)+C

3 0
4 years ago
Nicole wants to know the height of a snow sculpture but it is too tall to measure. Nicole measured the shadow of the snow sculpt
DaniilM [7]
10ft=120inch
120÷40=3 times
5ft ×3 =15ft(sculpture)
8 0
4 years ago
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The diagram shows a cube with sides of length 8 meters. A smaller cube with
Tanya [424]

Answer:

a) 512 cm^3

b) 469.125 cm^3

Step-by-step explanation:

8*8*8 = 512 cm^3

or

8^3 = 512 cm^3

3.5^3 = 42.875

512 - 42.875 = 469.125 cm^3

You can round the second answer down

5 0
3 years ago
Please help.i am really struggling
alina1380 [7]

Answer:

3,-3) becomes ; (3 + 5 , -3-12) ; (8,-15)

(7,-10) becomes;( 7 + 5, -10-12) ; (12,-22)

(13,-14) becomes (7 + 13, -14-10) ; (20,-24)

Step-by-step explanation:

What we have to do here is to add 5 to the x-axis value and subtract 12 from the y-axis value

(3,-3) becomes ; (3 + 5 , -3-12) ; (8,-15)

(7,-10) becomes;( 7 + 5, -10-12) ; (12,-22)

(13,-14) becomes (7 + 13, -14-10) ; (20,-24)

3 0
3 years ago
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